First-Order Integer-Valued Moving Average Process with Power Series Innovations

Authors

Eisa Mahmoudi^*, , Ameneh Rostami

Department of Statistics, Yazd University, P.O. Box 89175-741, Yazd, Iran

^*Corresponding author. Email: emahmoudi@yazd.ac.ir

DOI

10.2991/jsta.d.200917.001How to use a DOI?

Keywords

First-order integer-valued moving average process; Poisson thinning operator; Moving average model; Power series family of distributions

Abstract

In this paper, we introduce a first-order nonnegative integer-valued moving average process with power series innovations based on a Poisson thinning operator (PINMAPS(1)) for modeling overdispersed, equidispersed and underdispersed count time series. This process contains the PINMA process with geometric, Bernoulli, Poisson, binomial, negative binomial and logarithmic innovations which some of them are studied in details. Some statistical properties of the process are obtained. The unknown parameters of the model are estimated using the Yule-Walker, conditional least squares and least squares feasible generalized methods. Also, the performance of estimators is evaluated using a simulation study. Finally, we apply the model to three real data set and show the ability of the model for predicting data compared to competing models.

Copyright

© 2020 The Authors. Published by Atlantis Press B.V.

Open Access

This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Eisa Mahmoudi
AU  - Ameneh Rostami
PY  - 2020
DA  - 2020/09/28
TI  - First-Order Integer-Valued Moving Average Process with Power Series Innovations
JO  - Journal of Statistical Theory and Applications
SP  - 415
EP  - 431
VL  - 19
IS  - 3
SN  - 2214-1766
UR  - https://doi.org/10.2991/jsta.d.200917.001
DO  - 10.2991/jsta.d.200917.001
ID  - Mahmoudi2020
ER  -